## Example 57.8 Reading Mixed Model Results with Classification Variables

This example creates data sets that contains parameter estimates and corresponding covariance matrices with classification variables computed by a mixed regression model analysis for a set of imputed data sets. These estimates are then combined to generate valid statistical inferences about the model parameters.

The following statements use PROC MIXED to generate the parameter estimates and covariance matrix for each imputed data set:

```proc mixed data=outfish;
class Species;
model Length= Species Height Width/ solution covb;
by _Imputation_;
ods output SolutionF=mxparms CovB=mxcovb;
run;
```

The following statements display (in Output 57.8.1) the output mixed model coefficients from PROC MIXED for the first two imputed data sets:

```proc print data=mxparms (obs=10);
var _Imputation_ Effect Species Estimate StdErr;
title 'MIXED Model Coefficients (First Two Imputations)';
run;
```

Output 57.8.1 PROC MIXED Model Coefficients
 MIXED Model Coefficients (First Two Imputations)

Obs _Imputation_ Effect Species Estimate StdErr
1 1 Intercept   12.5356 2.7808
2 1 Species Bream -11.9103 3.5386
3 1 Species Pike 0 .
4 1 Height   -0.1605 0.5158
5 1 Width   7.3962 1.1365
6 2 Intercept   13.3607 2.7848
7 2 Species Bream -10.5204 3.0517
8 2 Species Pike 0 .
9 2 Height   -0.3139 0.4384
10 2 Width   7.4861 1.0005

The following statements use the MIANALYZE procedure with an input PARMS= data set:

```proc mianalyze parms(classvar=full)=mxparms;
class Species;
modeleffects Intercept Species Height Width;
run;
```

The "Variance Information" table in Output 57.8.2 displays the between-imputation, within-imputation, and total variances for combining complete-data inferences.

Output 57.8.2 Variance Information
The MIANALYZE Procedure

Variance Information
Parameter Species Variance DF Relative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
Between Within Total
Intercept   0.325023 7.632716 8.022743 1692.4 0.051099 0.049738 0.990150
Species Bream 0.307202 10.394843 10.763486 3410 0.035464 0.034815 0.993085
Species Pike 0 . . . . . .
Height   0.003686 0.217662 0.222085 10085 0.020320 0.020110 0.995994
Width   0.006488 1.097103 1.104888 80560 0.007096 0.007071 0.998588

The "Parameter Estimates" table in Output 57.8.3 displays the combined parameter estimates with associated standard errors.

Output 57.8.3 Parameter Estimates
Parameter Estimates
Parameter Species Estimate Std Error 95% Confidence Limits DF Minimum Maximum Theta0 t for H0:
Parameter=Theta0
Pr > |t|
Intercept   12.669835 2.832445 7.1144 18.22530 1692.4 12.004593 13.360690 0 4.47 <.0001
Species Bream -11.180159 3.280775 -17.6126 -4.74767 3410 -11.910303 -10.520395 0 -3.41 0.0007
Species Pike 0 . . . . 0 0 0 . .
Height   -0.246488 0.471259 -1.1702 0.67727 10085 -0.313882 -0.160511 0 -0.52 0.6010
Width   7.511074 1.051137 5.4509 9.57130 80560 7.396172 7.594860 0 7.15 <.0001